Internal Energy of a Gas Mixture – Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

Internal Energy of a Gas Mixture

A gas mixture consists of \(2\) moles of \(\text{O}_2\) and \(4\) moles of \(\text{He}\) at temperature \(T\). Neglecting all vibrational modes, total internal energy of the system is
\(11\text{ }RT\)
\(13 RT\)
\(15 RT\)
\(9 RT\)

Solution:

Internal energy \(U = n_1 \frac{f_1}{2} RT + n_2 \frac{f_2}{2} RT\). For diatomic \(\text{O}_2\), \(f_1 = 5\), and for monoatomic \(\text{He}\), \(f_2 = 3\). Thus, \(U = 2 \left(\frac{5}{2}\right) RT + 4 \left(\frac{3}{2}\right) RT = 5RT + 6RT = 11RT\).

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